In Eugene M. Izhikevich’s Neural Dynamics work, Integrators represent Neurons or computational models that accumulate incoming activity and fires an Action Potential when a threshold is reached. Essentially a signal summation mechanism.
While models of integrators go far back to the breakout work of hte Hodgkin Huxley and Morris Lecar models, they are most often represented as the classic Leaky Integrate And Fire model. These are the standard for neuromorphic computing platforms like intel’s loihi chip.
Usually in the context of a single neuron model like that of Morris Lecar/Hodgkin Huxley models, we see manifest as a Saddle Node on Invariant Circle bifurcation, meaning the attracting and repelling fixed points collide and annihilate.